Usually, in these cases you should wait at least 12months before re-applying.
There are basically 3 things you should do in order to increase your chances of getting as much interviews as possible, and if you want, I can help you with that:
1) Get a sponsor from Bain Office who can help you shorten the re-application timeframe and sponsoring you (I can provide you with the contact of a close friend of mine working in Bain Milan)
2) Get a referral from any other office and company you would like to apply now or in the future (that’s the key when it comes to increasing your chances to get an interview; also in this case I can provide you with several close friends working in other Milan-based top consulting companies like Strategy&, BCG, etc. also worldwide if your intention is to apply abroad)
3) Build a compelling, eye-catching and professional CV/resume and CL (this is also key to get the interview; I can help you with a deep analysis and provide you with a final revised CV structured based on a framework that has been successful in 85% of the cases)
In the end, to get the call for an interview is all about having a sponsor in the office and having a great CV!
Hope this helps